An analysis of the research literature on the effects of subjective attitude on visual perceptual constancy indicated that the most general and reliable effect stems from the individual's assumption that there are real and nonreal perceptual magnitudes. An assessment of perceptual capacity will have quite different outcomes depending on whether the individual is judging apparent or actual magnitudes and relationships. The outcome can be controlled on the average task instructions, but valid perceptual measurement in the individual case requires indirect methods of assessing response biases. A response bias model of time perception was applied to judgments of time made by subjects over periods of sleep. Previous studies of such judgments have produced equivocal relationships between the time sense and electronencephalographic and other variables. Two reasons for the equivocality were identified. First, average time estimates were idiosyncratic for individual subjects, bearing no relationship to the actual intervals or to EEG activity. Second, subjects often do not clearly remember the beginning of the time interval to be judged. When they do remember the beginning of the interval, there is a definite correlation of the time estimates with actual elapsed times over intervals of stage 1-REM (dreaming) sleep.